Renormalization by Birkhoff-Hopf factorization and by generalized evaluators: a case study. (English) Zbl 1253.81118
Consani, Caterina (ed.) et al., Noncommutative geometry, arithmetic, and related topics. Proceedings of the 21st meeting of the Japan-U.S. Mathematics Institute (JAMI) held at Johns Hopkins University, Baltimore, MD, USA, March 23–26, 2009. Baltimore, MD: Johns Hopkins University Press (ISBN 978-1-4214-0352-6/hbk). 183-211 (2011).
Summary: We compare different techniques used to evaluate divergent multiple sums and integrals, either being inspired by the Birkhoff-Hopf approach of Connes and Kreimer in quantum field theory renormalization or arising from generalized evaluators, as well as different procedures within the Birkhoff Hopf framework. We then apply this study to evaluate divergent Riemann integrals indexed by rooted trees and by rooted trees decorated by symbols.
For the entire collection see [Zbl 1243.14002].
For the entire collection see [Zbl 1243.14002].
MSC:
| 81T75 | Noncommutative geometry methods in quantum field theory |
| 81Q30 | Feynman integrals and graphs; applications of algebraic topology and algebraic geometry |
| 11M36 | Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) |
| 81T15 | Perturbative methods of renormalization applied to problems in quantum field theory |
